Abstract

We investigate analytically (by harmonic mode expansion) and numerically (by finite-difference-time-domain technique) the propagation of light pulses in photonic crystals in subdiffractive regimes. It is shown that in general the short pulses of narrow beams diffract more strongly than the corresponding monochromatic beams and disperse more strongly than the corresponding pulses of the plane waves. We also demonstrate coupling between the temporal dispersion and the spatial dispersion (diffraction) resulting in a complicated spatiotemporal evolution of the propagating pulses.

© 2007 Optical Society of America

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  1. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
    [CrossRef]
  2. D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres, and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003).
    [CrossRef] [PubMed]
  3. R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
    [CrossRef]
  4. M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
    [CrossRef]
  5. D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
    [CrossRef] [PubMed]
  6. L. Wu, M. Mazilu, and Th. F. Krauss, "Beam steering in planar-photonic crystals: from superprism to supercollimator," J. Lightwave Technol. 21, 561-566 (2003).
    [CrossRef]
  7. Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
    [CrossRef]
  8. Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
    [CrossRef] [PubMed]
  9. K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  10. H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
    [CrossRef] [PubMed]
  11. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]
  12. K. Staliunas, "Midband dissipative spatial solitons," Phys. Rev. Lett. 91, 053901 (2003).
    [CrossRef] [PubMed]
  13. S. Longhi, "Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals," Phys. Rev. E 71, 016603 (2005).
    [CrossRef]
  14. S. Longhi and D. Janner, "X-shaped waves in photonic crystals," Phys. Rev. B 70, 235123 (2004).
    [CrossRef]
  15. K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
    [CrossRef]
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  17. Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
    [CrossRef]

2007 (1)

Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
[CrossRef]

2006 (3)

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

2005 (3)

S. Longhi, "Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals," Phys. Rev. E 71, 016603 (2005).
[CrossRef]

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

2004 (3)

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

S. Longhi and D. Janner, "X-shaped waves in photonic crystals," Phys. Rev. B 70, 235123 (2004).
[CrossRef]

2003 (3)

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

Augustin, M.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Behrmann, G. P.

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Chen, C.

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

Chigrin, D. N.

Cojocaru, C.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

Enoch, S.

Etrich, C.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Herrero, R.

Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Huchs, H.-J.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Iliew, R.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

Illiew, R.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Janner, D.

S. Longhi and D. Janner, "X-shaped waves in photonic crystals," Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Kawakami, Sh.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Kley, E.-B.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Krauss, Th. F.

Lederer, F.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Loiko, Yu.

Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
[CrossRef]

Longhi, S.

S. Longhi, "Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals," Phys. Rev. E 71, 016603 (2005).
[CrossRef]

S. Longhi and D. Janner, "X-shaped waves in photonic crystals," Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Lu, Zh.

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

Marandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

Mazilu, M.

Murakowski, J.

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

Nolte, S.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Peschel, U.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Prather, D. W.

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

Pustai, D. M.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Schelle, D.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Schneider, G. J.

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

Schuetz, Ch. A.

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

Serrat, C.

Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Sharkawy, A.

Shi, Sh.

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

D. W. Prather, Sh. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, "Dispersion-based optical routing in photonic crystals," Opt. Lett. 29, 50-52 (2004).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

Sotomayor Torres, C. M.

Staliunas, K.

Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
[CrossRef]

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 (2006).
[CrossRef]

K. Staliunas, "Midband dissipative spatial solitons," Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Tayeb, G.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

Trull, J.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Tunnermann, A.

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

Venkataraman, S.

Wu, L.

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Appl. Phys. B: Photophys. Laser Chem. (1)

M. Augustin, R. Iliew, C. Etrich, D. Schelle, H.-J. Huchs, U. Peschel, S. Nolte, E.-B. Kley, F. Lederer, and A. Tunnermann, "Self-guiding of infrared and visible light in photonic crystal slabs," Appl. Phys. B: Photophys. Laser Chem. 81, 313-319 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and Sh. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Huchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tunnermann, "Diffractionless propagation of light in a low-index photonic-crystal film," Appl. Phys. Lett. 85, 5854-5856 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

Zh. Lu, Ch. A. Schuetz, Sh. Shi, C. Chen, G. P. Behrmann, and D. W. Prather, "Experimental demonstration of self-collimation in low-index-contrast photonic crystals in the millimeter-wave regime," IEEE Trans. Microwave Theory Tech. 53, 1362-1368 (2005).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (1)

Yu. Loiko, C. Serrat, R. Herrero, and K. Staliunas, "Quantitative analysis of subdiffractive light propagation in photonic crystals," Opt. Commun. 269, 128-136 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

S. Longhi and D. Janner, "X-shaped waves in photonic crystals," Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Phys. Rev. E (3)

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, "Subdiffractive light pulses in photonic crystals," Phys. Rev. E 74, 016605 (2006).
[CrossRef]

K. Staliunas and R. Herrero, "Nondiffractive propagation of light in photonic crystals," Phys. Rev. E 73, 016601 (2006).
[CrossRef]

S. Longhi, "Localized and nonspreading spatiotemporal Wannier wave packets in photonic crystals," Phys. Rev. E 71, 016603 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

H. S. Eisenberg, Y. Silberberg, R. Marandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

K. Staliunas, "Midband dissipative spatial solitons," Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

Zh. Lu, Sh. Shi, J. Murakowski, G. J. Schneider, Ch. A. Schuetz, and D. W. Prather, "Experimental demonstration of self-collimation inside a three-dimensional photonic crystal," Phys. Rev. Lett. 96, 173902 (2006).
[CrossRef] [PubMed]

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

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Figures (7)

Fig. 1
Fig. 1

Transverse dispersion curves for monochromatic waves in Type I (a) and Type II (c) PCs as obtained by numerical solution of Eq. (4) using the expansion in nine harmonics. Parameters are (a) m = 0.0695 , L x = Λ x λ 0 = 0.6 , L z = Λ z λ 0 = 0.985 and (c) L z = Λ z λ 0 = 0.49 , where Λ z = 2 π q ( Λ x = 2 π q ) is the longitudinal (transverse) period of susceptibility modulation. Dispersion curves for different values of the frequency near the ZD point for (b) Type I and (d) Type II; the frequency decreases from the top to the bottom curves with decrement δ ω = 0.03 ω 0 ( λ 0 = 800 nm ) . Solid red curves in (b) and (d) correspond to the dispersion curves at ZD points presented in the domains marked by dashed ellipses in (a) and (c), respectively.

Fig. 2
Fig. 2

Analytical results for ZD curves for monochromatic beams (a) [Eq. (6)] and the parameters (b)–(f) as obtained along ZD curves [Eqs. (8)]. These parameters describe the character of spreading of light pulses with central frequency on the ZD curves. Solid green (dashed blue) curves represent results for Type I (Type II) PCs. F old = m k 0 2 q 2 .

Fig. 3
Fig. 3

Spatial distribution of modulus of electric field of a pulse at input point (a) and at propagation distance 80 λ 0 in PCs of (b) Type I and (c) Type II. The parameters of the PCs are L z = 1.84 for Type I and L z = 0.40 for Type II PCs. The other two parameters of the PCs for both types are L x = 0.70 and m = 0.0695 . Ellipses indicate areas with low electric susceptibility. Initial transverse and longitudinal width of the input Gaussian pulses are (a) 2 w = 3 λ 0 and (b) 2 w = 1.875 λ 0 and (c) 2 w = 3 λ 0 and 2 w = 7.5 λ 0 . Temporal duration of input pulses (a),(b) t P = 5 fs and (c) 20 fs .

Fig. 4
Fig. 4

Evolution of transverse spatial width 2 w of input Gaussian pulses (blue solid curves) and Gaussian beams (red solid curves) in PCs of (a) Type I and (b) Type II. Pink short-dashed line is a guide line for spreading of transverse width of beam that is governed by the second-order diffraction, i.e., by the law 2 w z 1 4 [15, 17]. Long-dashed green curves correspond to monochromatic Gaussian beams in homogeneous media. The initial transverse and longitudinal widths of the input Gaussian pulses are 2 w = 3 λ 0 and 2 w = 1.875 λ 0 ( t P = 5 fs ) ; other parameters as in Fig. 3. The peak at the beginning stage of pulse propagation is caused by the projection into other (diffractive) Bloch modes.

Fig. 5
Fig. 5

Evolution of longitudinal spatial width 2 w (temporal duration) of the Gaussian pulses in PCs of Type I (blue solid curves) and Type II (red solid curves). Parameters are the same as in Fig. 4. Dashed line is the guide for pulse broadening governed by the law 2 w z .

Fig. 6
Fig. 6

Evolution of transverse 2 w width of the input Gaussian pulses (blue solid curves) and Gaussian beams (red solid curves) in PC of Type II under condition T 0 α > 1 . Parameters for the Type II PC are the same as in Figs. 4b, 5, but the pulse duration is t P = 20 fs ( 2 w = 7.5 λ 0 ) and initial transverse widths of the input Gaussian pulse and beam are 2 w = 3 λ 0 .

Fig. 7
Fig. 7

Dispersion/diffraction length of pulses propagating in PCs of Type II (solid curve with rhombs) and in homogeneous medium (dashed curve) in dependence on temporal duration of input pulse. Parameters for the Type II PC are the same as in Figs. 4b, 5, 6. Initial transverse widths of the input Gaussian pulses are 2 w = 3 λ 0 . The dispersion/diffraction length is calculated as the distance at which the transverse width of the pulse becomes larger than the initial width in 4 2 times (under such definition Rayleigh length is equal to 17.5 λ 0 ).

Equations (16)

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t ( B x B z D y ) = [ 0 0 z 0 0 x z x 0 ] ( H x H z E y ) ,
D σ = E σ ε 0 ε ( r ) , B ρ = H ρ μ 0 .
A ρ ( ω 0 , x , z ) = j , l A ρ ( j , l ) e i k , j x + i k II , l z e i ω 0 t ,
[ k 0 2 ( k , j 2 + k II , l 2 ) ] E y ( j , l ) + m k 0 2 u = ± 1 , v = ± 1 E y ( j + u , l + v ) = 0 ,
K 2 = k 2 ( q 2 + q II 2 ) , K II = ( k II 2 k 0 2 ) ( q 2 + q II 2 ) ,
Z = z ( q 2 + q II 2 ) 2 k 0 , X = x ( q 2 + q II 2 ) .
f = m k 0 2 ( q 2 + q II 2 ) , Q II = 2 q II k 0 ( q 2 + q II 2 ) ,
K II = 2 f 2 ( 1 Q II ) + K 2 ( 8 f 2 [ 1 ( 1 + Q II ) q II 4 k 0 ] ( 1 Q II ) 3 1 ) .
8 f 2 = ( 1 Q II ) 3 [ 1 ( 1 + Q II ) q II ( 4 k 0 ) ] .
K II = K II , 0 + δ ω V 0 + δ ω 2 W 0 + α δ ω K 2 + O ( ε 6 ) .
K II , 0 = ( 1 Q II , 0 ) 2 ( 4 B ) ,
1 V 0 = ( 1 Q II , 0 ) ( 4 3 Q II , 0 ) ( 4 B ) ,
1 W 0 = Q II , 0 ( 4 3 Q II , 0 ) ( 4 B ) ,
α = 3 Q II , 0 ( 1 Q II , 0 ) + q II ( 4 B k 0 ) ,
B = [ 1 ( 1 + Q II , 0 ) q II ( 4 k 0 ) ] .
A Z = ( i K II , 0 1 V 0 T i W 0 2 T 2 + α T 2 X 2 ) A = 0 .

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